Electrical-sonic transducers



Jan. 12, 1960 M. GREENSPAN ET'AL ELECTRICAL-SONIC TRANSDUCERS Filed NOV. 21, 1957 ATTORNEYS United States ELECTRICAL-SONIC TRANSDUCERS Martin Greenspan, Silver Spring, Md., and Raymond M. Wilmotte, Miami, Fla.

Application November 21, 1957, Serial No. 697,971

11 Claims. (Cl. 179-1) The present invention pertains to transducers, and may be further characterized as relating to the field of interconverting electrical and sonic energy. The term sonic energy is used herein in its broadest sense, and does not indicate frequencies restricted to the audible range, but rather is intended to describe the form of the energy concerned. In fact, it is contemplated that the presentinvention will find its greatest utility in the field of ultrasonics.

` In accordance with one aspect of the present invention, an electrical-sonic transducer, or transducer for interconverting electrical and sonic energy, is provided, wherein a plurality of discrete transducing elements interconnect an electrical energy carrying line with a sonic energy carrying line. For example, the electrical line may be an electrical delay line, while the sonic line may be any material capable of carrying sonic energy therealong, such as a piezoelectric material. The discrete electrical-sonic transducer elements, which may for example be magnetostrictive or piezoelectric in character, are individuallyV sonically coupled to the sonic line and individually electrically coupled to the electrical line at -spaced intervals along said lines. The successive transducer coupling points in the electrical line are spaced from each other, in terms of electrical energy delay time along the electrical line, by amounts substantially equal to the corre-l sponding transducer coupling points in thesonic line, in

terms of lsonic energy delay time along the sonic line. In other words, the couplings are so located on the respective lines that upon an input signal being applied to one line, when it reaches the lirst transducer coupling it is coupled into the other line, and thereafter the two signals travelling on their respective lines reach each corresponding coupling point substantially in phase. This` general character of transducer is herein identified as a distributed transducer. Its overall object is to convert a signal of one form of energy to the other, and the resultant output is appliedV to a load responsive to the form of the converted energy.

A distributed transducer of the general character above.A described is disclosed in U.S. Patent 2,702,472 to Jacob Rabinow. In the distributed transducer there described, the individual transducers are all equal in dimension, and the principal purpose of that distributed transducer is to effect a substantial increase in the power output at the load above that obtainable with a single transducer element. It should be observed that in the distributed transducer described in said Rabinow patent, the frequency response of the system at the load is the same as that had with but a single transducer element of the chosen dimension, namely the power absorbedby the load is proportional lto the square of the frequency (amplitude ilat with frequency). In accordance with the present invention, however, the distributed transducer is provided with transducer elements having different dimensions, and preferably operated near their resonant frequencies. By this means a great variety of frequency response character-v 2,92l,l34 Patented Jan. 12, 196).v

ice

istics at the load is obtainable, and of particular interestv is the fact that by this teaching a system of transducerv element relationships is available whereby a substantially flat power response over a broad band of frequencies is obtainable with but a relatively few transducer elements having appropriately chosen dimension relationships, as will be more fully described hereinafter.

In accordance with a further aspect of the present invention, an electrical-sonic transducer is provided wherein at least half the power introduced in the output line is delivered to the load. We have discovered that the proportion of power delivered to the load in the output line is a function of the spacing of the discrete transducer element from the load end of the line, and such spacing. is related to the frequency of applied signal. As willV be more particularly described hereinafter, the spacing of the transducer element from the load can be chosen to obtain in the load at least one half the power in theY output line.

It is accordingly one object of the present invention to provide a distributed transducer affording a great variety of frequency-response characteristics.

Another object of the present invention is to provide a distributed transducer for interconverting electrical and sonicv energy affording a great variety of frequency-V response characteristics.

will become apparent to those skilled in the art from a consideration of the following detailed description thereof had in conjunction with the accompanying drawings, wherein:

Fig. 1 is a schematic representation of a distributed transducer embodying one form of the present invention;

Fig. 2 is a schematic representation of a distributed transducer embodying a second form of the present invention;

Fig. 3 is a schematic representation of a single element transducer utilized to illustrate the principles of the invention embodied in Figs. 1 and 2, and also to illustrate an additional feature of the present invention; and

Fig. 4 is an equivalent circuit diagram of the transducer shown in Fig. 3.

For the purpose of illustration in the following specific description of the invention, the input to the transducer is considered to be electrical into the electrical line, and the output is considered to be sonic into a load placed at one end of the sonic line. However, it should be understood that the invention is equally applicable to the inverse situation where the input is sonic energy applied to the load end of the sonic line, delivering an electrical output at the input end of the electrical line. Also, the individual transducer elements are illustrated as piezoelectric means, however it should be understood thatV magneto-strictive means or other electrical-sonic interconverting means may be employed.

In Figs. l and 2 two basic embodiments of the present distributed transducer are illustrated.

while in Fig. 2 the invention is shown as a corresponding distributed thickness expander. First, considering the 'y form of the invention illustratedin Fig. 1, an electricali input from any'desired source or generator 19, such as an 1n Fig. 1 the in! vention is illustrated as a distributed length expander@ oscillator; a voice` transmitter, or the like, is had at 10,

and from there applied toY any suitableandl conventionaly electrical delay line 11, as are well known in the art.

The delay line is tapped at'a plurality of points a, b, c, andd andi the outputs therefrom coupled? into? 'amplifiers 112:2, 12b, 12e, andf12d.- Associated witli'theel'ectr-ical' line'. 111 is a sonic line 14, whichmay convenientlyfbeformed from piezoelectric material, liavingI asonic energy absorber 17y at one end and a sonic energyy output load? bef formed. of course as acomp'osite by using'. a' plurality.

"angina .fr e

ofaseparate piezoelectric" transducers interconnected byV any inactive' materialcapable of functioning as: aA sonic. line, and whose characteristic' impedancey is thesame as the piezoelectric material in the transducers. Tecomplete= the; present distributed transducer, the; amplifiersY 12a, 1'2b;,12'c, and 12d are coupled to'therespective trans'- ducer electrodes 13a, 13b, 13C and 13d. The electrodes.

13a, 13b, 13C, and'13dhave,.as shown, ditferentlengthdimensions along the line 14y resulting in. diiferentlength. dimensions for the discreet transducer; elementsw defined.

hyll said-electrodes.

In Fig. 2, the invention is shown in the form of a distributedV thickness expander. As in the preceding em'- bodiment, an electrical input from generator 29, or the like, is applied at `26 and fed to an electrical delay line 211. A sonic line Ztl-having an absorber 27' at one end and a load 26 at its other end, containsga plurality of individual piezoelectric transducer elements 26W, 26x, 26y, and 26z. 1 The transducer elements are-shown crosshatched. In this embodiment these transducer elements are inserted in the sonic line lengthwise thereof, rather than across the line as in Fig; 1. Accordingly, the dimensions of each transducer element are shown to diifer in their thickness dimension, rather than in the length dimension as inV Fig. 1. In the present embodiment, a's in Fig.` 1, the sonic line between the transducer elements, and

to the lo-ad 26 and absorber 27, i.e., the uncross-hatched areas, may be formed of piezoelectric material, in which case the polarity of the uncross-hatched area elementsy are all opposite to the polarity of the cross-hatched transducer elements, or the uncross-hatched areas may be formed of an inactive material having the same characteristic impedance as the piezoelectric material. To cornplete the present distributed transducer system by interconnectingy or coupling the electrical line 2-1. with the. sonic line 24, the electrical delayline 21 is tapped at a plurality of points w, x, y, and z, and the electrical. outputs therefrom are co-upled through the respective ampliers 22W, 22x, 22y, and 22z to electrodes 23W, 23x, 23y, and 23z, respectively, of piezoelectric transducers 26W,

26x, 26y, and 26z. The opposite electrodes of'the trans-' ducers are coupled to ground at 25.

In both of the foregoing embodiments of the invention,

the spacing of the individual transducer elements in the sonic line and the spacing'of the corresponding taps in the electrical line are selected, so that the time delay in. sonic energy travel between successive transducer ele ments in the sonic line is 'substantially equal to the time delay in electrical energy travel between successive corresponding taps in the electrical delay line. `Accordingly,.

in Fig. 1 for example, an electrical input signal applied a't10 enters the electrical delay line 11 and travels there along. When it reaches tap a, the signal is passed by amplier 12a to piezoelectric transducer electrode 13a and coupled into the sonic line 14. The resultant sonic:l signal travels from transducer 1321 both to the left and right along line 14; The energy travelingto the.' left isv eventually absorbedin absorber 17. As the sonic energy travels to the. right toward load 16, the original electrical 'to ield.v and .to motion.

input signal is traveling to the right along line 11. The time7 delay for electrical' energy: alongl line 11V between taps a, b, c, and d is so chosen as to equal substantially the time delay for sonic energy along line 14 between transducer elements 13a, 13b, 13C, and 13d. Accordingly, the electrical signals on delay line 11 reach tap b substantially in phase with the sonicsignals reaching transducer element 13b, and the samer in phase relationship between the two AsignalY trains vcontinues for tap 'c and transducer element 13e, and tap d and transducer element 13d. Finally; the sonic energy. on line 14 is coupled into load. 16 as the outputy ofthe distributed transducer. The present Vdescription; offoperation of the distributedY transducer of Fig. l is equally applicable to the embodiment o`f`Fig. 2. Since the correspondence therebetween is readily apparent, repetition of the operation with specic reference to Fig. 2 is deemed unnecessary.

It is next desired to consider a summary mathematical analysis of the output characteristics of the distributed transducer ofthe present invention. To facilitate an underst'andingv of this analysis and; illustrateethe significance of the symbols there employed, reference isihad to- Figs@ 3- and-4, Fig; 3 showing a single element transducer'inthe thickness expander formV of the invention, and Fig. 4' being an equivalent circuit diagram of the transducerI system of Fig. 3. InvFig; 3 theelectrical input from generator or the like 39 is at 30. Since there is onlyl one active or piezoelectric transducer element 36 here employed, an electrical delay line is not needed. Ther inputv feeds to one electrode 33 of the transducerv element 36,. whose second electrode is coupled to ground at 35.V The element 36 is located in al sonic line 34 similar to lines 14 and 24 in Figs. l and 2, terminating at one end ina vsonic absorber 37 and at the other end in a sonic load 36. As' depicted in the drawing, the value of the input signal is denoted V, the thickness of the active element or transducer element 36 is T, whose right end isr a distance, d" from the load; 36. The characteristic impedance ofthe active element 36, the absorber 37, and the'inactive portions of thesonic linev are all denoted as Z0. The impedance'of the load 36 is denoted ZL. iIn the equivalent` circuit of Fig.r 4, that part to the right of the dashed' line isr thel equivalent T network (see Terman, Radio Engineers Handbook, p. 195, McGraw-Hill, 1943) of theV inactive material betweenV the transducer element andthe load;

v a:- A (2) The input 15V is the driving voltage V referred to the mechanical' side, 1 being the turns ratio of the fictive,-

electromechanical transformer. For a thickness eX- pander A dA l 45:@ Y (3) and fora lengthI expander. i Y Y Y Y :Eg Y (4.).

In Equations 3 and 4, d is the, piezoelectric modulus Aap.;

propriate to the cut, sE 'is the isagric compliance appro.- priate tothe types ofmotion, A is cross section, T is: thickness parallel to motion, and w is width perpendicular.-

Thestatic capacitance. of the., transducer is consideredabsorhedin.thedlay line Whh,

sin tie-Hw sm -sm see Equation 2, so that the bandwidth is independent of the load;

(3) The phase of the load current varies with frequency in a manner independent of the load, the phase dependingy only on "otziw-rd) A (6)4 that is, on the distance from the center of the active element to the load, and on frequency.

The foregoing mathematical analysis of a single active element thickness type expander can be applied to a multielement thickness expander. In the case of a two-element thickness expander, one element of thickness T1 and distance d1 from the load, and a second element of thickness T2 and distance d2 from the load, with'V, and V2 denoting the driving voltages, from Equation 5 itl can be derived that see Equation 6. is the centertocenter distance between the active elements. With V2 delayed relative to V, by the time the phase of V2 relative to V, is

l l w8 e?? and Equation 7 becomes from which, considering Equation 2,

hA-ZOTalmsm 2c+2|v2|sm 2c 9) Equation 9 is readily extended to a transducer of any number n of elements, giving Y 2 n T; llLl-mtsllal SID 2 `(10) Although derived with specic reference to a thickness expander, it is apparent that Equation l0 is equally ap` plicable-to a length expander, in which case T denotes length instead. of thickness. If the thicknesses (or lengths) T, in Equation l0 are integral multiples of the smallest length T1, Equation l0 is a Fouriers sine series for |iLl, so'that a widevarety of re'sponse curves can be synthesized by suitable choice .of IVXI. The constants gb, are not disposable. For the length expander of Fig. 1, they are all equal,.see Equation 4, and for .the thickness expander of Fig. 2, they are inversely proportional `ti) thickness, see equation 3.

If Equation 10 is applied to a conventional distributed transducer wherein all the transducer elements `possess the same dimensions, as in the case of the distributed transducer described in the aforementioned patent to Jacob Rabinow, it will be seen that the power response is restricted to being proportional to the square of the frequency (amplitude is flat with frequency). When theindividual transducers are small relative to the sonic energy wavelengths,

for all i, so that sin 2c 2c and Equation 10 becomes, if |V|=|VI and for all I I |a|= 2 l L-W' @-3 l being the total active length. Thus, the power response is proportional to the square of the frequency (the am-A plitude is at with frequency) so long as where A is the wavelength of sonic energy in the transducer material. The load current for an n-element transducer is n times as great (the power output is n2 times as great) as from a single-element transducer.

In the case of the instant invention, however, which is concerned with distributed transducers having transducer elements of dilerent dimensions in the system, the power' response with frequency possibilities are numerous and varied. Of particular interest is the specific example where the power response with frequency is made lat. In the case of a thickness expander, if one makes T=T odd), that is:

T1=T, T2=0, 113:31', etc.

substituting Equation 3 in Equation 12, and if [Vil={V], then 12V| M t aT lul-204.21, s1ST=1" t 1,' sm 2? (12) The sum in Equation 14 is the Fouriers series for The greater the value of n, the atter is the power re-l sponse with frequency. In the case of a length expander, as in Fig. 1, p does not depend on T, but the same results can be achieved by making [V1] inversely proportional to'v T1. Thus, in the case of a length expander, if one makes T=i17 (i odd)that is (T is length of transducer plate 13a, 13b, 13e, and 13d in Fig. 1) substituting Equation 4 in Equation l2, which is" a constant (independent of frequency), Equation 12 becomes, if

From the foregoing it will be appreciated that by the present invention a great variety of output power withv frequency response characteristics can be obtained, and av speciicY desired characteristic can be obtained by selecting an appropriate sequence of dimensions for the several active transducer elements inthe sonic line. Also, inne.`

cordance with the present invention, it is'considered that for most applications it will bepreferred-that the dimensions of the transducer elements be -selected in accordance with the applied signals, to afford operation thereof at or near a resonant frequency, or that the transducer elements have resonant frequencies intermediate' the'limits of the band of applied signals. By this means innumerable outf put power with frequency response curves maybe obtained, including a flat curve as one specific desirable curve.

An additional feature of the vpresent'Y invention resides in the fact that in the case of a single element transducer, by appropriately positioning the transducer element with respect to the load, at least one half of the radiated power from the transducer system can be obtained: at: theload". It is obvious that the absorber current iA corresponding to some particular transducerelement depends on the distance of the element fromrthe load and on the load impedance, for iA is'the sum of the'c'urrent radiated' directly toward the load and that reected therefrom. The ab-V sorber current iA can be shown to bedefrned by the equation in the case of a single element transducer illustrated in Figs. 3 and 4. From Equation 5, the load current iL in this'case has its maximum absolute value {ibo} whenever t'is an odd multiple of Y 2 t the midband' points, the absorber current is'from Equation 14 so"that the power expended Vatthe absorber'at these points` is Pno- ZuZ L for the ratio of power expended inthe absorber to that in the load atmidband. The minimum'value (quafunctionof 1,0) of the expression 202 e052 2+ZL2 stazza in Equation `17 is 202 or ZL2, whichever is smaller. Thus,

if ZL Z0, tp is chosen so that cos2 Ztl/:1, which from Equation 1 means that d (see Fig. 3) is an^even number of quarter wavelengths, and the relationship results that P A Z0 1 19 P1410 ZL On the other hand, if ZL Z0, 5b is chosen so that sin2 Ztl/:1, which means that d (see Fig. 3) is an odd number of quarter wavelengths, and the relationship results that PLrO Z0 From the foregoing it is apparent that in; an instance where the characteristic impedance of the sonic line Z0 isless' thany the impedance of the-'load ZL, by'placing the transducer element a distance d'fromxtheload equal. to-

.any even numbery of' transducer midband quarter. wave.

from the sonic -line will appear in the yload. And similarly, in an instance where the characteristic impedance of thegsonic line Z0 isgreaterthan'th'e impedance of the load ZL, by placing the transducer element ajdista'nce d from the load equal to any odd number of transducer midband quarter' wavelengths from the load, at least onev half the power radiated from the sonic line will appear intheload. i Y" d Y In the foregoing detaileddescription 'of 'the present invention, reference is had to certainfspeci'c structural features in order to"facilitate a complete' understanding of the invention. It is not, however,V` intended tol limit the scope of theV invention to such specific features, and it is understood that modifications, variations and equivalents thereof will be apparent to those skilled in the art. Accordingly, such 'structures as aelembrace'dwithin the spirit and terms of the following claims are considered to b ewithin the vscope' of the' present invention.

We claim l. An electrical-sonic distributed transducer compris?.

ing an electrical delay line, a sonic delay line, one line having an input end, the' other! line having an output end, a plurality of electrical-sonic' transducer elements individually sonically' coupled into said sonic' line and in# dividually electrically Icoupled into said electrical line, with the-sonic delay Vtime along said sonic line between said elements being substantially equal vto the electrical delay time alongv said electrical line betweenthe same ones of said elements, and at least some of said elements' havingk substantially different dimensions to provide substantially different resonantf frequencies.

2. An electrical-sonic distributed transducer comprising an electrical delay line, a sonic delay line, one `line having an input end, the other line having an outpu't'end', a plurality of electrical-*sonic transducer elements individually sonically coupled into said sonic line in an orientation forming a distributed.thickness expander,.said elements also beingindividually electrically coupled into said electrical line, with the' sonic delay time along said sonic line between said elements being substantially equal to the electrical delay time along said electrical line between the same ones of said elements, and at least some o'. said elements having substantially different dimensions to provide substantially dilerent resonant frquencies.

3. An electrical-sonic distributed transducer4 comprising an electrical delay line, a sonic? delay line, oneline having an input end, the other line having an output end, a plurality ofl electrical-sonic transducer elements vindividually sonically coupled into said sonic line in an orientation forming a distributed length expander, saidr elements also being individually Velectric-ally coupled intoy of said elements having substantiallyY diierentdimensions to provide substantially different resonant frequencies.

4. An electrical-sonic distributed transducer comprisling an electrical delay line, ai sonit'delyline, one line having an input end, the other line having an output end, aplurality. ofelctricalfsonic' transducerv elements individually sonically. coupled into' said sonic lineand inf dividually electrically'` coupled. into". said electrical' line,` with the; sonic delaytirne alonglsai'd so'nic`fline'between said elements: beingd substantially 'equa-Lto the electrical delay time along electricalllin betweenthe samef ones of Vsaid' elements; Yat 'lealstz somef ofv saidfy elements having different' 'resonant frequencies; means" for apply# ing .a signal input lto said input end, s'ai'd signal? occupy!4 lengths from the load', atleast onehalfzthapowen *radiated-z; 15 inga determinedff'requeney' band, Vand-said elenientslhav.-A

ing substantially different dimensions to provide substantially resonant frequencies intermediate the limits of said frequency band.

5. An electrical-sonic distributed transducer comprising an electrical delay line, a sonic delay line, one line having an input end, the other line having an output end, a plurality of electrical-sonic transducer elements individually sonically coupled into said sonic line in an orientation forming a distributed thickness expander, said elements also being individually electrically coupled into said electrical line, with the sonic delay time along said sonic line between said elements being substantially equal to the electrical delay time along said electrical line between the same ones of said elements, at least some of said elements having different resonant frequencies, means for applying a signal input to input end, said signal occupying a determined frequency band, and said elements having substantially diderent dimensions to provide substantially resonant frequencies intermediate the limits of said frequency band.

6, An electrical-sonic distributed transducer comprising an electrical delay line, a sonic delay line, one line having an input end, the other line having an output end, a plurality of electrical-sonic transducer elements, individually sonically coupled into said sonic line in an orientation forming a distributed length expander, said elements also being individually electrically coupled into said electrical l-ine, with the sonic delay time along said sonic line between said elements being substantially equal to the electrical delay time along said electrical line between the same ones of said elements, at least some of said elements having different resonant frequencies, means for applying a signal input to said input end, said signal occupying a determined frequency band, and said elements having substantially different dimensions to provide substantially resonant frequencies intermediate the limits of said frequency band.

7. An electrical-sonic distributed transducer comp-rising an electrical delay line, a sonic delay line, one ine having an input end, the other line having an output end, a plurality of electrical-sonic transducer elements individually sonically coupled into said sonic line and individually electrically coupled into said electrical line, with the sonic delay time along said sonic line between said elements being substantially equal to the electrical delay time along said electrical line between the same ones of said elements, at least some of said elements having different resonant frequencies, and said last named elements having dimensions lengthwise of the sonic line bearing a ratio to each other of odd multiples of the smallest stated dimensions of the last named elements.

8. An electrical-sonic distributed transducer comprising an electrical delay line, a sonic delay line, one line having an input end, the other line having an output end, a plurality of electrical-sonic transducer elements individually sonically coupled into said sonic line and individually electrically coupled into said electrical line, with the sonic delay time along said sonic line between said elements being substantially equal to the electrical delay time along said electrical line between the same ones of said elements, at least some of said elements having different resonant frequencies, said last named elements having dimensions lengthwise of the sonic line bearing a ratio to each other forming a series of consecutive odd multiples of the smallest stated dimension of the last named elements.

9. An electrical-sonic transducer comprising a sonic delay line, an electrical-sonic transducer element sonically coupled into said delay line, an electrical line electrically coupled to said element, one line having a signal input at an end thereof and the other line having a signal output at an end thereof, said transducer element being located a distance from said end of said sonic delay line substantially equal to an integral multiple of a quarter wavelength of a midband frequency of said element.

10. An electrical-sonic transducer comprising a sonic delay line, an electrical-sonic transducer element sonically coupled into said delay line, an electrical line electrically coupled to said element, one line having a signal input at an end thereof and the other line having a signal output at an end thereof, said transducer element being located a distance from said end of said sonic delay line substantially equal to an integral odd multiple of a quarter Wavelength of a midband frequency of said element.

11. An electrical-sonic transducer comprising a sonic delay line, an electrical-sonic transducer element sonically coupled into said delay line, an electrical line electrically coupled to said element, one line having a signal input at an end thereof and the other line having a signal output at an end thereof, said transducer element being located a distance from said end of said sonic delay line substantially equal to an integral even multiple of a quarter wavelength of a midband frequency of said element.

References Cited in the tile of this patent UNITED STATES PATENTS 2,702,472 Rabinow Feb. 22, 1955 2,717,981 Apstein Sept. 13, 1955 2,806,155 Rotkin Sept. 10, 1957 

